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A particle moves from a point $(-2\hat{i} + 5\hat{j})$ to $(4\hat{j} + 3\hat{k})$ when a force of $(4\hat{i} + 3\hat{j})$ N is applied. How much work has been done by the force?
A
5 J
B
2 J
C
8 J
D
11 J
Explanation
$W = \vec{F}\cdot\Delta\vec{r}$.
Detailed Solution
Displacement $\vec{s} = (4\hat{j} + 3\hat{k}) - (-2\hat{i} + 5\hat{j}) = 2\hat{i} - \hat{j} + 3\hat{k}$
$W = \vec{F}\cdot\vec{s} = (4\hat{i} + 3\hat{j})\cdot(2\hat{i} - \hat{j} + 3\hat{k}) = 8 - 3 = 5$ J
$W = \vec{F}\cdot\vec{s} = (4\hat{i} + 3\hat{j})\cdot(2\hat{i} - \hat{j} + 3\hat{k}) = 8 - 3 = 5$ J